Question

let f, g R=R be defined as f(x) =3x-5 and g(x) =x+5/5 . find fog and gof​

Answer 1

Step-by-step explanation:

fog(x)=f{g(x)}

=f(x+5/5)

=3(x+5/5)-5

=3(x+1)-5

=3x+3-5

=3x-2

gof(x)=g{f(x)}

=g(3x-5)

=(3x-5)+5/5

=3x-5+1

=3x-4

Answer 2

Given data:

$f,g:\mathbb{R}\to\mathbb{R}$

$f(x)=3x-5$, $g(x)=\dfrac{x+5}{5}$

To find:

$fog$ and $gof$

Step-by-step explanation:

First we find $fog$

Here, $fog=f(g(x))$

$=f(\dfrac{x+5}{5})$

$=3(\dfrac{x+5}{5})-5$

$=\dfrac{3x+15-25}{5}$

$=\dfrac{3x-10}{5}$

Now we find $gof$

Here, $gof$

$=g(f(x))$

$=g(3x-5)$

$=\dfrac{3x-5+5}{5}$

$=\dfrac{3}{5}x$

Answer:

• $fog=\dfrac{3x-10}{5}$

• $gof=\dfrac{3}{5}x$

Note:

In order to find $fog$ and $gof$, we have to write $g$ and $f$ as functions of $x$ respectively.

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